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Similar expressions
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Solving integrals/ (3x^2)*(e^-x^3)

Integral of (3x^2)*(e^-x^3) dx

The solution

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 oo             
  /             
 |              
 |          3   
 |     2  -x    
 |  3*x *e    dx
 |              
/               
2

$$\int\limits_{2}^{\infty} 3 x^{2} e^{- x^{3}}\, dx$$

Integral(3*x^2/E^(x^3), (x, 2, oo))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 3 x^{2} e^{- x^{3}}\, dx = 3 \int x^{2} e^{- x^{3}}\, dx$
1. Let $u = e^{- x^{3}}$ .
  
  Then let $du = - 3 x^{2} e^{- x^{3}} dx$ and substitute $- \frac{du}{3}$ :
  
  $\int \frac{1}{9}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{3}\right)\, du = - \frac{\int 1\, du}{3}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $- \frac{u}{3}$
  Now substitute $u$ back in:
  
  $- \frac{e^{- x^{3}}}{3}$
So, the result is: $- e^{- x^{3}}$
Add the constant of integration:

$- e^{- x^{3}}+ \mathrm{constant}$

The answer is:

$- e^{- x^{3}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                        
 |         3             3
 |    2  -x            -x 
 | 3*x *e    dx = C - e   
 |                        
/

$$-e^ {- x^3 }$$

Simplify

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The answer [src]

 -8
e

$$3\,\left({{e^ {- 8 }}\over{3}}-{{e^ {- {\it oo}^3 }}\over{3}} \right)$$

 -8
e

$$e^{-8}$$

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Use the examples entering the upper and lower limits of integration.

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Integral of (3x^2)*(e^-x^3) dx

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